论文标题
非线性未知输入可观察性和未知输入重建：一般分析解决方案
Nonlinear Unknown Input Observability and Unknown Input Reconstruction: The General Analytical Solution
论文作者
论文摘要
可观察性是任何动态系统的基本结构特性，并描述了重建从观察其输入和输出来表征系统的状态的可能性。尽管竭尽全力研究此属性并引入分析标准能够检查动态系统是否满足该属性，但当动态也由未知输入驱动时，没有一般的分析标准可以自动检查状态可观察性。在这里，我们介绍了这个基本问题的一般分析解决方案，通常称为未知输入可观察性问题。本文提供了此问题的一般分析解决方案，即，它基于自动计算（分化和矩阵等级的确定）提供系统的过程，从而使我们能够自动检查状态可观察性，即使存在未知输入（算法6.1）。本书的第二部分中提出了这个问题的第一个解决方案：“可观察性：基于不变性群体的新理论” [45]。本文提出的解决方案在[45]中完成了先前的解决方案。特别是，新的解决方案详尽说明了不属于“相对于其未知输入的经典”系统类别的系统。分析推导很大程度上利用了[45]中引入的几个新概念和分析结果。最后，作为这里获得的结果的简单结果，我们还为未知输入重建问题提供了答案，该问题与状态可观察性问题密切相关。我们通过研究视觉惯性传感器融合框架中非线性系统的可观察性特性来说明新算法的实现，该框架的动力学是由两个未知输入和一个已知输入驱动的。
Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from observing its inputs and outputs. Despite the huge effort made to study this property and to introduce analytical criteria able to check whether a dynamic system satisfies this property or not, there is no general analytical criterion to automatically check the state observability when the dynamics are also driven by unknown inputs. Here, we introduce the general analytical solution of this fundamental problem, often called the unknown input observability problem. This paper provides the general analytical solution of this problem, namely, it provides the systematic procedure, based on automatic computation (differentiation and matrix rank determination), that allows us to automatically check the state observability even in the presence of unknown inputs (Algorithm 6.1). A first solution of this problem was presented in the second part of the book: "Observability: A New Theory Based on the Group of Invariance" [45]. The solution presented by this paper completes the previous solution in [45]. In particular, the new solution exhaustively accounts for the systems that do not belong to the category of the systems that are "canonic with respect to their unknown inputs". The analytical derivations largely exploit several new concepts and analytical results introduced in [45]. Finally, as a simple consequence of the results here obtained, we also provide the answer to the problem of unknown input reconstruction which is intimately related to the problem of state observability. We illustrate the implementation of the new algorithm by studying the observability properties of a nonlinear system in the framework of visual-inertial sensor fusion, whose dynamics are driven by two unknown inputs and one known input.
